// Log-normal arithmetic parameterization? Not! what van Hecke used.
twoway (function y=lnnormalden(x,ln(0.1)-0.5*ln(1/.1^2+1),sqrt(ln(1/.1^2+1))), range(0 4)) ///
	(function y=lnnormalden(x,ln(0.5)-0.5*ln(1/.5^2+1),sqrt(ln(1/.5^2+1))), range(0 4)) ///
	(function y=lnnormalden(x,ln(1)-0.5*ln(1/1^2+1),sqrt(ln(1/1^2+1))), range(0 4)), title("LogNormal, d ~= 0.5")

postfile kwpower test d T dfm dfr using kwpowermcln2.dta, replace
quietly forvalues d=0.1(0.05)0.5 {
	noisily display "difference " `d'
	forvalues i=1/2500 {
		clear
		set obs 60 // group size = 20
		generate group = mod(_n, 3)+1
		generate sigma = sqrt(log(1+1/(group*`d')^2))
		generate mu = log(group*`d')-0.5*sigma^2
		generate y = exp(rnormal(mu, sigma))
		anova y group
		post kwpower (1) (`d') (e(F)) (e(df_m)) (e(df_r))
		kwallis y, by(group)
		post kwpower (2) (`d') (r(chi2_adj)) (r(df)) (.)
	}
}
postclose kwpower

use kwpowermcln2.dta, clear

generate sig = Ftail(dfm, dfr, T)<0.05 if test==1
replace sig = chi2tail(dfm, T)<0.05 if test==2
*tabulate test sig, row
bysort test: tabulate d sig, row

collapse (mean) sig, by(test d)
separate sig, by(test)
label variable sig1 "Anova"
label variable sig2 "Kruskal-Wallis"
save kwpowermcln2table.dta, replace
line sig1 sig2 d, title("Log-Normal, by MC") ytitle("Power") ///
	xtitle("group differences")